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Bulletin of the American Physical Society

Quantum Phase Transition in Interacting Quantum Wires

Mehul Dixit, Tobias Meng, Markus Garst, Achim Rosch, Julia S. Meyer

Published Mar 22, 2011• 0 citations
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We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have made it possible to enhance the interaction between the electrons. Here we show that hitherto unexplained anticrossing between conduction energy subbands, observed in such experiments, can be explained through a simple yet effective discretized model which undergoes a second-order quantum phase transition within the Ising universality class. Accordingly, we observe how the charge distribution, transverse to the direction of the wire, will vary across the phase transition. We show that data coming from three different samples with differing electron densities and gate voltages show a remarkable universal scaling behavior, determined by the relevant critical exponent, which is only possible near a quantum phase transition.
We investigate the impact of noisy environments on transport through a one dimensional interacting quantum wire containing a scattering impurity. The impurity is known to induce a metal-insulator quantum phase transition as a function of the interaction strength in the wire. By considering Ohmic-class environments (ranging from Ohmic, to sub-Ohmic and super-Ohmic cases), we elucidate the influence of fluctuations on this phase transition. Within a perturbative renormalization group approach, we show that Ohmic environments keep the phase transition intact, while sub- and super-Ohmic environments, modify it into a smooth crossover at a scale that depends on the interaction strength in the wire. The system, however, still undergoes a metal-to-insulator-like transition when moving from sub-Ohmic to super-Ohmic environment noise. We further consider realistic experimental conditions due to finite length and finite temperatures of the wire, and explore the signatures of the phase transition in the temperature dependence of the impurity-induced back-scattering electrical conductance.